Square wave

The square-wave signal and the rectangular wave refers to a periodic signal that switches between two values ​​back and forth, in a graph having a rectangular curve over time. It can be unipolar or bipolar occur.

The rectangular signal heard in the sound generator in synthesizers to the basic forms and has a " hollow " sound character because only odd integer multiples of a fundamental frequency are generated, called harmonics, which is why it is often used as a basis for imitation of flutes and brass instruments.

Signals with ideal rectangular course exist only in theory. The edges can not rise vertically and thus perform an infinitely steep jump; Instead, the real leap describe the rise and fall times. Inter alia due to the capacitive and inductive behavior of the transmission lines has a square wave signal on a common under-and overshoot.

The duty cycle is insignificant for consideration as a digital signal; However, it influences the DC value and the proportion of the harmonics.

Generation

A square-wave signal is generated either by an astable multivibrator, generally with a square-wave generator, or from a different signal form by means of a Schmitt trigger.

An additional time- symmetric signal is obtained at a stable frequency by frequency halving. For transmission as an AC voltage (ie without a DC component ) makes it possible symmetrical square-wave voltage in the voltage level is symmetrical.

And crystal oscillators usually give off a square wave which is used for example as a clock signal for a microprocessor. However, the quartz crystal itself leads from a sine wave.

Any other forms (for example, for measurement purposes ) are now generated with function generators using direct digital synthesis (DDS).

Properties

Square wave signals are characterized by the following features:

  • Frequency and period
  • Duty cycle: He is in a symmetrical square wave 50 %, and may otherwise be in the range between 0 and 100 %.
  • Low- and high- level ( for example, unipolar with 0 and 5 volts for TTL circuits )

A further feature in the digital technology, the jitter, that is, the time deviation occurring between the pulses and the frequency stability.

Use

Wave signals are the basis of digital signal processing. Square waves (ie periodic rectangular signals ) occur, inter alia:

  • As a clock signal for digital processors and controllers
  • As a pulse width modulated signal with sensors, digital -to-analog and analog - to-digital converters, switching regulators and switch mode power supplies and Class -D audio amplifiers
  • At the output of the pulse and function generators for laboratory purposes
  • In synthesizers as one of the fundamental forms, often with adjustable pulse width modulation
  • As a simple digital sound signal that can be generated ( such as tones for devices, children's toys)

Spectral observation

The square wave having a single frequency can be regarded as a superposition of sine waves with an infinite number of frequencies.

Fourier analysis

Fourier analysis enables by using a mathematical method, the decomposition of a signal into sine and cosine functions. Under the assumption of an ideal and symmetrical square wave signal with no DC component yields the following Fourier series:

The peak value h of the square wave with a fundamental frequency f and base circle frequency ω = 2? f and the time t. The formula shows that the frequency spectrum of a symmetrical square wave signal consists only of odd harmonics, which can be measured with a spectrum analyzer. The amplitudes of the harmonics decrease with increasing frequency.

Fourier synthesis

Now, if the process is reversed and a Fourier synthesis performed, but the result is not an ideal square wave signal.

Rather, the Fourier series expansion leads to a waveform in which the signal appeared before and after the jump points under the lower (imaginary ) pulse top and overshoots the upper ( imaginary) pulse top.

This phenomenon is known as Gibbs phenomenon and should not be confused with the above-mentioned lower and overshoot, but is often referred to as well.

The lack of in practice, non-transferable high frequency components due to the rounding at the discontinuities. A ripple in the pulse top is it hardly caused.

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